In his statement, Mr. Scott warned that failure to comply would result in fines and the possible revocation of a facility’s license.

Lauren Schenone, the governor’s press secretary, said the rules were effective immediately and would last 90 days, after which they could be renewed. She said that Mr. Scott would “fight aggressively” to put the rules into law, and that the rules do not include state support to pay for what could end up being daunting expenses.

“It is our expectation that these facilities will do everything they can to protect lives,” she said.

In response to criticism over the home’s attempts to get the government to help, a spokesman for Mr. Scott has said the calls made to the governor were referred to the state Agency for Health Care Administration and the Florida Department of Health and quickly returned.

Florida requires nursing homes to ensure emergency power in a disaster as well as food, water, staffing and 72 hours of supplies. A new federal rule, which will not be enforced until November, adds that the alternative source of energy must be capable of maintaining safe temperatures. But it does not specify that the source of energy must be a generator, or that the energy source must power air-conditioning.

The nursing home under scrutiny in Florida had a generator, but it did not power the air-conditioning. Hurricane Irma had affected a tree that apparently hit the transformer that powered the cooling system, leading to fatally hot conditions in the home.

Overhauling health care rules — even after problems arise from natural disaster — can prove challenging. Hospitals and nursing homes have sometimes pushed back against requirements, arguing that they are costly, unnecessary and a particularly crushing burden on smaller homes.

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In a telephone interview on Saturday, Martin Goetz, the chief executive of River Garden Senior Services, a nursing home in Jacksonville that did not lose power or air-conditioning, said the governor’s newly imposed requirements would be “impossible” for many homes to comply with in such a short time.

“What I think nursing homes will do is buy a lot of fans,” he said. “You can’t just go triple and quadruple generating capacity.” Doing so, he said, takes planning, reviews and approvals — all of which takes time.

The governor, Mr. Goetz added, is “shooting from the hip” and choosing to require more resources, when in fact, “the problem at the Hollywood facility was a failure of management.”

Robert E. Solomon, a division manager at the National Fire Protection Association, said the emergency rules also seemed “like the kind of thing that normally would have to go through a public rule-making process.”

“The idea and intent is worthy,” he said, “but that is a lot of generator capacity, design, installation and inspection to complete in 60 days.”

Others welcomed the rules. Gail Coleman, who runs Gail’s Assisted Living Facility in Tampa, said that they were “a good idea” and that she planned to buy a generator. Her home, with eight residents, lost power for four days after the storm. “Times like these you find out exactly what you need and should get,” Ms. Coleman said.

Dr. David Marcozzi, an associate professor at the University of Maryland School of Medicine who helped develop the federal rule, praised the governor’s action.

“I think this is a bold move by the governor,” Dr. Marcozzi said. The Florida rules set “firm requirements and provides needed specificity to protect residents and patients,” he said.

Kristen Knapp, a spokeswoman for the Florida Health Care Association, an advocate for nursing homes, said her group was reviewing the rules. Gail Matillo, president and chief executive of Florida Argentum, which represents assisted living communities, said the industry was still evaluating the rule’s impact and had several questions for regulators.

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On Friday, a state senator filed legislation that would require nursing homes and assisted-living facilities to have working generators. A similar bill collapsed in the State Legislature in 2006, in the aftermath of Hurricane Wilma, when it met with strong industry opposition.